Question

For every integer n, if n² is not divisible by 4, then n is ________.

1) even
2) odd
3) prime
4) negative

Answer 1

If n² is not divisible by 4, n is odd.

Step-by-step explanation:

For every integer n, if n² is not divisible by 4, then n is odd. To understand why, we need to consider the divisibility rules for 4. A number is divisible by 4 if the last two digits of the number are divisible by 4. However, for an odd number, its square will always have a last digit of 1, 5, 9, or 6, which are not divisible by 4. Therefore, if n² is not divisible by 4, n must be odd.